This paper proposes a two-part design method for unity-feed back linear multivariable systems withstableplants. First, a known algebraic technique yields a matrixQ, with the property that the family ofexponentially stableandproper Q globallyparametrizes the family ofexponentially stableclosed-loop systems withpropercontrollers. Second, having obtained such a family ofQs, a non-linear programming problem is formulated, which when solved, will yield thebest feasible Q, with respect to designer-specified objective and constraint functions. The method developed makes possible thesystematic formulationandsolutionof a class of design problems which representpracticaldesign considerations as inequality constraints in non-linear programming problems. Severalnewdesign problem formulations are given, and then solved, for some specific plants. These formulations include, for example, constraints to avoidplant saturation, and the mixing oftime and frequencydomain objectives and constraints.